Book on discrete mathematics for self study I am searching for book on discrete mathematics which is suitable for self study. This mean I want it to have exercises with answers (It would be ideal if it had solutions). I have already read "Discrete Mathematics" of Kenneth Ross. I have also partially read "Concrete Mathematics" of Knuth but I didn't like the style much. I am searching for next book to read. I do not have any requirements on topics I just want it to cover few of them like combinatorics and counting, recurrences and probably generating functions. 
 A: Epp's text on Discrete Mathematics is a very nice read. Johnsonbaugh is good as well, but is more technical and more geared towards computer scientists.
Nicholas Loehr's text Bijective Combinatorics is a great read for the topics you listed, which fall in the realm of combinatorics. Loehr's text is rigorous and thorough, but it is also very well written and intuitive. I did my undergraduate work at Virginia Tech where he teaches, and he has a reputation for being both brilliant and a fantastic instructor. His book lives up to that reputation, in my opinion.
Make sure you avoid Alan Tucker's Applied Combinatorics textbook. It's a horribly written book, and the only redeeming quality are the exercises.
A: "generatingfunctionology"
by Herbert S. Wilf
and
"A=B"
by Marko Petkovsek, Herbert Wilf and Doron Zeilberger.
These are available
as free downloads at
https://www.math.upenn.edu/~wilf/DownldGF.html
and
https://www.math.upenn.edu/~wilf/AeqB.html
A: I'm taking a Discrete Mathematics course right now, using Applied combinatorics by Roberts and Tesman. It does have some good 'real life' examples and applications. 
A: Here are very complete notes and problem sets from Jacob Lurie's (Harvard) combinatorics course (Harvard).
http://www.math.harvard.edu/~lurie/155.html
